chapter 18: waiting line analysis Flashcards
when do waiting lines occur?
when there is a temporary imbalance between supply (capacity) and demand
downsides of waiting lines
add to the cost of operation
they reflect negatively on customer service
loss of goodwill
loss of business due to customers refusing to wait and going elsewhere
queueing theory
a mathematical approach to the analysis of waiting lines
Why Is There Waiting?
arrival times and service durations exhibit a high degree of variability
the system at times becomes temporarily overloaded, giving rise to waiting lines; at other times, the system is idle because there are no customers
The goal of queueing analysis
to minimize total costs
The two types of costs in a queueing situation
“cost” of customers waiting for service
cost of provision of capacity
ways management can reduce their customers’ perception of the waiting time
- Determine the acceptable wait time for the operation
- Try to keep the waiting time experienced by a customer consistent over time
- Install distractions that entertain and involve customers
- Inform the customer of the cause of an abnormal wait and peak times
- Keep the line moving continuously
- Use first come, first served discipline (fairness is important)
- Allow customers to serve themselves
- Prepare the customers for service before the actual service
- Make people conscious of time only if they overestimate the wait time.
- Keep staff who are not serving customers out of sight.
- Try to segment customers by personality
- Never underestimate the power of a friendly and attentive server
ways in which management can reduce waiting times by fixing the system constraints
Use temporary workers
Shift demand
Standardize the service
Look for a bottleneck
Model choice is dependent on which characteristics of the waiting line system under investigation
- Potential number of customers.
- Number of servers and structure of queueing system.
- Arrival and service patterns.
4 . Queue discipline (i.e., order of service).
an infinite source of customers situation
the potential number of customers greatly exceeds system capacity
a finite source of customers situation
When the potential number of customers is limited
Each server in the queueing system can handle how many customers at a time?
can handle one customer at a time
queueing system can have how many servers?
single or multiple serνers
true or false
Another distinctive of the queueing system characteristic is the number of steps or phases in a queueing system
true
advantage of a joint line of people waiting leading to multiple servers
first come first serve (fairness)
wait time will be less
disadvantage of a joint line of people waiting leading to multiple servers
which type of customers would prefer it
it might appear too long
may take a large space
servers may not work as fast as if they were responsible
for their own line
customers cannot choose their favorite server
homogeneous customers would prefer it
advantages of separate lines leading to servers
which type of customer would prefer this
reduces the total variability of service durations, resulting in a reduced average wait time for all customers
heterogenous customers
The most commonly used queueing models assume that the customer arrival rate can be described by which distribution?
The Poisson distribution
The Poisson distribution
a one-parameter discrete probability distribution of the number of events occurring in an interval of time
–> provided that these events occur with a known average rate and independently of the time since the last event
The exponential distribution
a one-parameter continuous probability distribution of the times between events that happen continuously and independently at a constant average rate
reneging
customers grow impatient and leave the line
jockeying
customers switch to another line
balking
customers decide the line is too long and, therefore, do not enter the line
Queue discipline
the order in which customers are served
Operations managers typically look at which four measures when evaluating existing or proposed queueing systems
- The average number of customers waiting, either in line (not counting those being served) or in the system (including those being served)
- The average length of time customers wait, either in line or in the system
- Server utilization
- The probability that an arriving customer will have to wait for service or will have to wait more than a specified length of time before being served
Server utilization
the proportion of time a server will be busy
reflects the extent to which the servers are busy rather than idle
why would operations manager not necessarily want 100% server utilization?
increases in server utilization are achieved at the expense of greater increases in the average customer wait time
average customer wait time becomes exceedingly large as server utilization approaches 100 percent
100 percent utilization of servers leads to burnout
which server utilization proportion is the most adequate?
between 80% and 90%
the simplest queuing model
why?
model 1: Single Server, Exponential Service Durations
a system that has one server (or a single crew)
the queue discipline is First Come First Serve
customer arrival rates can be approximated by a Poisson distribution
service durations by an exponential distribution
Model 3: Single Server, Constant Service Durations
a queueing system with constant service durations (and Poisson arrival rates)
–> to cut the average number of customers waiting in line in half (relative to Model 1)
Model 5: Multiple Servers, Exponential Service Durations
poisson arrival rates with average tent symbol and exponential service durations with average 1/u
all M servers work at the same rate
customers form a single waiting line
the multiple server formulas are more complex than the single server formulas for Lq and Po.
when does a multiple server system exist?
whenever there are two or more servers working individually to provide service to customers
customer waiting cost
costs incurred by the organization due to customer waiting
The optimal capacity (usually in terms of number of channels)
one that minimizes the sum of customer waiting costs and capacity or server costs
Minimize total cost = Total average customer wait cost + Total server pay cost
what is used to identify the capacity size that will minimize total costs?
An iterative process
Because the total cost curve is U-shaped, what does it mean for the total cost
the total cost will initially decrease as capacity is increased, and then it will eventually begin to increase
Once it begins to increase, additional increases in capacity will cause it to continue to increase
